1. Event “zero-time” determination with TOF detector
F. Pierella for the TOF-Offline Group
INFN & Bologna University
PPR Meeting, January 2003

2. Overview Previous results Present results
Summary of algorithms and conclusion
Plan

3. Statistical algorithm
By assigning a mass configuration to n selected tracks in a given event, we can require a best fit condition thus deriving
the most probable mass configuration for the n tracks, out of the possible N=3n and
the corresponding most probable zero-time for the event.

4. Previous results

5. Reminder Previous result has been obtained
with a smearing on MC momentum in order to take into account the momentum resolution (no reconstructed momentum used);
with a gaussian smearing on track length given by GEANT (=30ps);
with a gaussian smearing on MC time-of-flight;
matching contamination was not included.

6. Present results Included full simulation
Tracks assigned to a “wrong time” are now included in the statistical (combinatorial) method (so contamination is now included); in order to minimize this effect, we select tracks with momentum 1.25GeV/c<p<1.75GeV/c which is the best range for track matching;
No (coarse) Gaussian Smearing on MC time-of-flight is used but full TOF detector simulation (edge effect, efficiency, and resolution simulation) is now considered;
Reconstructed momenta are now used for zero-time calculation.

7. Present Results

8. CPU Timing for the statistical method
Considering the combinatorial character of the algorithm, the CPU computing time for the zero-time determination is reported in the following table
Number of tracks
per set
CPU computing time
n=10
5
n=15
50

9. Summary of the algorithms and conclusion
Statistical method:
no dependence from particle ratios
event zero-time resolution of the order of 30ps
The pion mass assumption for all tracks has been suggested as an alternative –and faster- method to calculate the event zero-time, but in this case a dependence from particle ratios occurs

10. Dependence from particle ratio
Simplified case with only pions and kaons

11. Dependence from particle ratio

12. Plan
Plan is to use a GA (Genetic Algorithm) for event “zero-time” determination;
The architecture of GA systems allow for a solution to be reached quicker since “better” solutions have a better chance of “surviving” and “procreating”, as opposed to randomly throwing out solutions and seeing which ones work

13. “Definition” of the problem
In the GA dictionary of the “zero-time” problem
the “chromosome” corresponds to a mass configuration of the n selected tracks in the event;
a “chromosome allele” corresponds to a mass assignment to a given track;
the “fitness value” of a given “chromosome” corresponds to the chi-square of the mass configuration;
the “parent selection” is done according to the “fitness value”;

14. Strategy
“offspring chromosomes” are obtained “crossing-over” the “father” and “mother” “chromosomes”;
generally, the fitness values of the “offspring chromosome” are better than those of the “parent chromosomes”;
“mutation” corresponds to a random change of a mass assignment in a given mass configuration;
mutations can occur leading to “more performing chromosomes”
for systems where the population is larger (say 50) the fitness levels should more steadily and stably approach the desired level.